Racquet Mod Formulas: Matching Specs

Roughly two weeks ago, I posted a thread with an emberassingly simple system for attaining a given balance point, with given weights. Well, the original idea behind it's complete, and here it is:

Given a final weight, balance, swingweight, and one (1) added mass, it will spit out the location of the necessary added masses, as well as the added weight of the other concentrated mass. Checked with Steve H.'s original Racquet Mod excel sheet. All figures in metrics.

[EDIT]
The Spreadsheet has been updated to include some traits I thought important.

If you look a few replies down (the third, I believe) then you'll see that Travler suggested a few things I should add, and this is one: Instructions.

Begin by plugging in the values for the top three white squares, with the labelled amounts for the racquet you're using. For my DNX 10, I labeled them.

340
31
320

In that order. Do not add units! If you don't know off hand the specifications of your racquet, then check TW's info on it.
Next, in the next set of whited-out boxes, enter the intended specifications of your racquet, with all said and done. For instance, to go with the specs in the spreadsheet by default, I wanted to go with the 'Sampras setup' listed by TravlerAjm. That required a weight of 384 g, a 32 cm balance, and a swingweight of 367.
The fourth whited-out box in that section, labeled 'Weight 1 Mass,' you can enter just about any number lower than the total added mass in grams. If you're not sure how much mass you're adding the spreadsheet provides you with that piece of information. What this is, is the amount of weight to add at the first spot, or 'location 1.'

Afterwards, it will spit out a few numbers: The important ones are cells C23 and C24, though future variations on this spreadsheet will make use of the final recoilweight, polarization, and so forth, in a more central role.

A Note On The Effect Of Specifications:Weight or Mass will change the static weight, and the punch on your volleys, but little else.Balance will have a distinct effect on the feeling of your racquet, wether it feels like it plows through the ball or gets pushed around by it. This is measured in CM from the butt of the racquet.Swingweight is a measure of the difficulty of swinging the racquet, but it is also a factor in the power level of the racquet: higher swingweight, higher power.Recoilweight is a measure of how much the racquet yields to the incoming ball. More means less. A flat hit shouldn't need much of this, due to the 'plowing' nature of the shot, where a windshield-wiper forehand will probably need more considering that it pretty much absorbs the ball's incoming speed.Effective Mass is a measure of how much mass is used when the racquet hits the ball. It's not intelligible, at this point, but it makes for a good reference point of how much your power will be changed.Polarization Index is a measure of how spread out your weight is. The higher the polarization index, the spinnier your racquet will tend to be. (Explained in the link)

If either value for 'weight location' comes out as greater than the total length of your racquet, you need to modify your input 'Weight 1 Mass.'

Well, for instance, say you're adding 12 grams total. You might enter as mass 1 anywhere from '1' to '11' and that's how much weight you would add at the location specified for mass 1. It's really just a reference number, like that most classic of variables, x.

The choice of how much weight to add at location 1 or 2 is purely your choice. In the creation of this, I made a simpler calculator, using set masses, then added in variability afterwards.

It doesn't make a huge difference, but your swingweight position factor of 10.16 should be 10. Swingweight is typically measured on machines that have a pivot point 10 cm up from the buttcap, not four inches up from the buttcap.

Ohhh? I used The Physics and Technology of Tennis as my reference. It refers to the swingweight being measured from four inches. So if you have a problem, take it up with Messr's Brody, Lindsay, and Cross. I do, but I just worked around it. (specifically, their change-in-swingweight formula was HORRIBLY inaccurate, but for the simplest of reasons.)

Now, AJK1, that sounds like a pretty agressive statement. Back it up. Give me exacts. I want my output to be statistically perfect, so give me numbers. Give me examples.

EDITED TO ADD MORE STUFF:

If my formula's wrong in theory, then I challenge you to provide me a better one. It'll probably take you about a day. If only in technicality, then where is my fault? I worked a lot harder on my product than you did on your trolling, so you cite your facts.

And if I come off as offended, it's only because AJK1 decides to come in, and instead of questioning my choice of any specific thing, like Greg did, I can't dissent because he hasn't said anything, he's just slandered my work without proof. I apologize if I came off as rude, or prudish, or whatever.

Thanks, Punisha. As much as I don't like being randomly trolled, I rarely expect to agree with AJK, and I enjoy the challenge, so no problems there. However, I was a little sheepish about sharing, so I'm glad that most folks are so supportive.

Okay, you DEFINITELY can't do it with your specs, then. I'd change the mass for 'Weight 1 Mass' until I got an answer in which both numbers are below the total length of the racquet.

Effective mass is, basically, how much weight the racquet uses when hitting the ball. At this point, the equation's totally buggered, but consistent, so I'd use it more for comparison purposes than anything else.

Recoilweight is how much the racquet recoils. Theoretically, you want less of this if you're a flat-hitter (the transfer of motion is direct; the way you swing the racquet plows without the need for recoilweight) and more if you're spinny (exact opposite).

Amone, i don't have to justify my statements to you or anyone else, i am not trolling, i'm stating what i know based on my close working partnership with my racquet technician. I am entitled to post comments here as much as you are, just because you don't like it, is not my problem. I don't want other members here taking what so-called "experts" you and travlerajm post as gospel, since my tech says a lot of it is nonsense. A lot of it has holes in it as stated by me and other readers, and if i see a problem, i'll make an objection. I'd much rather consult Greg Raven on racquet issues, as he obviously knows what he is talking about. It's his business! Not a bunch of high-school science kids sitting in their bedrooms on the computer.

Instead of "effective mass", I like to use the "hitting weight." Interestingly, the simple definition of hitting weight that I use correlates well with Cross's results for "rebound power," even though Cross never seems to make the connection in his papers.

The hitting weight HW = M*(R - 4), with M = static weight in kg, and R = distance to balance point in cm (the 4cm offset is the location where the racquet handle intersects with the extension of the forearm). The hitting weight gives you a very accurate measure of a racquet's power level due to the weight distribution.

If you take any 2 racquets with the same hitting weight, same stiffness, and same tension/stringlength ratio, they will have approximately the same coefficient of restitution.

Amone, I appreciate the work and look forward to any further fine tuning! What would be neat would be a way to plug in specs, including pre-modded, to figure out the hitting wieght that travlerajm speaks of.

And does increasing the static weight really only affect volleys? I thought this also affected a racquets stability, but I'm guessing that this factor is better represented in the recoilweight and as such static weight loses much of it's meaning?

I have a spreadsheet I've been using for a couple of years now to help me match racquets. The results of my spreadsheet correspond with the on-line tool Crawford Lindsey developed for USRSA members at racquettech.com. However, if I plug the same numbers into each of our spreadsheets, there are differences in the results.

I'm curious as to how your derived your formula for Effective weight (AKA Hitting weight). I have a completely different formula, which yields completely different results.

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The hitting weight is mathematically derived using the momentum balance, assuming that the swing has only translational motion at impact (neglecting the rotational component of the swing).

It is highly accurate for predicting power level on groundstrokes, because groundstrokes hit with sound technique have minimal rotational motion at impact. The correction factor to account for the Serve/Groundstroke Power Ratio (SGPR) must be applied to accurately predict relative power on the serve, because the serve has a large rotational component. If two racquets have the same hitting weight, but one has a longer balance, the power level will be about the same on groundstrokes, but the frame with the longer balance will generally be more powerful for serves.

The derivation of the formula for hitting weight is as follows.

We assume the impact of the ball on the racquet causes the racquet to pivot about the wrist joint, and that the racquet is otherwise constrained by the wrist joint (i.e., we neglect momentum losses transferred into the forearm). Let’s also neglect the momentum contribution of the hand to keep this simple.

The ball’s rebound momentum is determined by balancing the moments of the momentum vectors about the wrist joint.

Let’s define variables:

m = mass of ball
v = change in velocity of ball during impact
V = change in velocity of racquet center of mass during impact
r = distance from butt to point of impact
M = mass of hand
R = distance friom butt to balance point
d = distance from butt to wrist axis of rotation (about 4cm for a forehand, or 8cm for a 2hb).

The momentum balance is given by:

M*(R – d)*V = m*(r – d)*v

Rearranging gives:

M*(R – d) = m*(r – d)*(v/V)

m*(r – d) is a constant (neglecting any changes in sweet spot location due to weight distribution), and v/V is the ratio of the ball’s change in velocity to the racquet’s change in velocity. Clearly, v/V is a measure of the power level of the racquet.

@ AJK1: The assertion that I have ever tried to put myself forth as an expert is fallacious. I'm a high school student, at a public high school near Detroit. I've made no claim at any of my own knowledge, except this one piece of work, which is a work in progress. All my other assertions are made on other people's word which I believed above yours.

However, you haven't the right to assert anything without proving it. So if you won't prove it, then keep your mouth shut.

@ Nikolah: Static Weight may have an effect on stability, but I think that there is no direct correlation. Consider, for instance, the effects of adding 4 oz to the butt end of your racquet. I've done it before, it doesn't add any considerable stability or power. In fact, I lost some stability. So take that idea with a grain of salt.

@ Duzza: The locations are measured in CM from the butt end, and they're the center of mass. So if you were to add the weight in 4 inch strips, you'd start 2 inches below the reccomended position. I'd also suggest rounding up to one decimal place, so that it's easier to find.

@ Greg Raven: As I've said a few times, I'm not done yet, because my formulae are the tiniest bit off. I don't see where it is, but I know it's there because in my tests, my swingweight usually ended off by about .23 points, hence not perfect. And the Effective Mass formula is calculated badly somewhere, I don't know where. I got it right on paper, but on Excel I had trouble with it. So regarding that issue: Agreed. Effective Mass is wrong.

As to my formulae in the rest of the spreadsheet, I think they need some tweaking, and I don't know why yours say so differently (as the difference is pretty huge) but they are pretty close.

Amone- I like what you're doing with the spreadsheet. Keep up the good work and try not to get discouraged by any negative feedback.

I apologize if the rest of my post is slightly off-topic for the thread. I'm hoping that it could lead to a better understanding of the application of the formulas which are being discussed.

travlerajm said:

The hitting weight is mathematically derived using the momentum balance, assuming that the swing has only translational motion at impact (neglecting the rotational component of the swing).

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travlearjm- I've been adjusting the lead on my LM Radicals to try different things. I decided to put more lead on the handle (18 grams, to be exact), but I wrapped it too high. The center of mass is above the 4 cm line, which when using your formula leads to a relatively high hitting weight. This explains what I noticed when hitting with it yesterday, chiefly that it was equally (possibly more) powerful after adding weight to the butt than before, which struck me as odd before I read this post. I had thought that adding the weight should reduce power and it didn't. When I introduced the hitting weight formula to my spreadsheet, I noticed that the 18g didn't reduce the hitting weight at all. So that now makes sense.

The question I have is related to something I saw you mention a while back, in your Sampras setup post - that, at a certain point, increasing swingweight will begin to increase spin (due to ball flattening). My desire is to achieve a higher level of spin on the racquet. Is this measure of ball flattening an actual product of swingweight, or is it more related to the ratio of hitting weight to swingweight? Looking at the numbers, it seems to me that if you have two racquets with the same swingweight, the one with lower hitting weight should be more adequate for hitting a ball with more spin. Do you have a direct formula for calculating this ball-flattening, and what are your general thoughts on this?

Amone, i don't have to prove anything to you, my racquet tech's knowledge is all the proof i need. To other kids on these boards you might sound important and smart, but to me you and your statements are just full of holes. Even Greg Raven is telling you it's all wrong, your figures suck.

Ha ha ha, AJK. You're funny. If you wanted to play tagalong with Greg, you should've said so. I would've argued less, because he has a point which I have agreed with repeatedly. I don't need to sound smart, I just need to be useful. If I can give someone an answer, then my job's done. And you know what? This gives them that answer, in a public way that you don't give.

Your role is only that of the destroyer, dissenting and questioning with nothing other than a desire to dissent and question, no facts or realities. At least Greg has a contribution to make. I'm done with this discussion, I hope. Though you know, I am a young one, my fiery tempermentality might get me back in.

Excuse me, I was wrong. Silly me and my quick replies. I don't even need to be useful to you folks. I started the project for my own purposes, just like the reason I've been a keen follower of Travler's 'lectures,' same as I've read JohnCauthen's old posts, same as I took physics class this year to try to understand the things they don't talk about, and make my own decisions. I just like the feeling I get inside when people say 'Thanks Amone,' so I shared my own tool.

Amone, i don't have to prove anything to you, my racquet tech's knowledge is all the proof i need. To other kids on these boards you might sound important and smart, but to me you and your statements are just full of holes. Even Greg Raven is telling you it's all wrong, your figures suck.

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AJK1 - I hate to respond to such a blatant flame, but weren't you the one who several weeks ago posted that adding weight to the butt of a racquet reduced the swingweight (a blatantly and obviously false statement)? To me that brings your credibility into question when you accuse someone else of making statements that are "full of holes". Did you get that info from your racquet tech as well? And honestly, I don't know why you're coming after Amone here. I don't really see him making any bold statements - he's simply taken formulas provided by others and tried to make a spreadsheet for people to more easily utilize said formulas. Where's the harm in that? If, as you say, this is all horribly false information, then at worst people who try to use it will waste a few dollars on lead tape and then abandon the experiment. Your point seems to be that this is all worthless; if that's the case, then you probably don't need to post anything other than "This info is worthless". You've used a lot more space but you really haven't said anything other than that. So, essentially, you think this is worthless. Ok, I think we get it.

travlearjm- I've been adjusting the lead on my LM Radicals to try different things. I decided to put more lead on the handle (18 grams, to be exact), but I wrapped it too high. The center of mass is above the 4 cm line, which when using your formula leads to a relatively high hitting weight. This explains what I noticed when hitting with it yesterday, chiefly that it was equally (possibly more) powerful after adding weight to the butt than before, which struck me as odd before I read this post. I had thought that adding the weight should reduce power and it didn't. When I introduced the hitting weight formula to my spreadsheet, I noticed that the 18g didn't reduce the hitting weight at all. So that now makes sense.

The question I have is related to something I saw you mention a while back, in your Sampras setup post - that, at a certain point, increasing swingweight will begin to increase spin (due to ball flattening). My desire is to achieve a higher level of spin on the racquet. Is this measure of ball flattening an actual product of swingweight, or is it more related to the ratio of hitting weight to swingweight? Looking at the numbers, it seems to me that if you have two racquets with the same swingweight, the one with lower hitting weight should be more adequate for hitting a ball with more spin. Do you have a direct formula for calculating this ball-flattening, and what are your general thoughts on this?

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I have a similar question/curiosity. I recall your mention of that, but I'd like to know how much the measure of that flattening there should be, because I'd like to know how to make the racquet powerful-- and flat, not spinny.

I corrected myself with the SW thing, to say hitting weight, so what's your point? And i do give facts, eg. you're formulas are wrong for a start! Oh, and can you guys learn to spell properly, trying to get credibility is much harder when you show people you can't spell.

One other thing my friends, you think i flame, troll etc, well the reason i get annoyed with this high school garbage is because if you are going to post info on these boards, make damn sure it is correct. If it is correct, i will praise you, otherwise, make a mistake, correct it, get it right, or don't post.

That's acceptable, AJK, but it's trolling when I say that I tested it, and it's close enough that you won't know the difference, and you won't back up your assessment that it's junk. That's where the difference is. The only reason I bothered to reply is because you sounded like you genuinely didn't understand.

I corrected myself with the SW thing, to say hitting weight, so what's your point?

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I think my point was simple and quite clear. You're saying that you don't like people posting incorrect stuff; I pointed out a mistake which you made. People told you what was wrong and you fixed it. What you've done is say that Amone is wrong without offering anything to help him improve it. You haven't even said what exactly you thought was flawed about it. Amone's biggest obvious mistake was that he used 10.16cm instead of 10cm; Greg Raven pointed it out, not to sharpshoot Amone's post, but to help him make a more accurate spreadsheet. That's the difference between what your posts are and what his posts are.

AJK1 said:

And i do give facts, eg. you're formulas are wrong for a start! Oh, and can you guys learn to spell properly, trying to get credibility is much harder when you show people you can't spell.

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I assume you're including me in this spelling comment, though I can't fathom why. I'm sure I've made a few spelling errors from time to time, but I don't think I'm exactly firing off a litany of them such that my credibility is going to be tarnished. FWIW, I can clearly see 4 errors in usage/grammar on your part in that one small quote, which is somewhat ironic considering the message.

@ Duzza: The locations are measured in CM from the butt end, and they're the center of mass. So if you were to add the weight in 4 inch strips, you'd start 2 inches below the reccomended position. I'd also suggest rounding up to one decimal place, so that it's easier to find.

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so you're saying to add Half the weight(23 grams) to both positions, 10 and 36 cm above buttcap?

The hitting weight is mathematically derived using the momentum balance, assuming that the swing has only translational motion at impact (neglecting the rotational component of the swing).[...]

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If you look at the results from my spreadsheet, you'll see that I know what hitting weight is. On the OP's spreadsheet, however, I don't understand where that hitting weight is calculated, what the units of measurement are, and why his results are so different from mine.

[...]@ Greg Raven: As I've said a few times, I'm not done yet, because my formulae are the tiniest bit off. I don't see where it is, but I know it's there because in my tests, my swingweight usually ended off by about .23 points, hence not perfect. And the Effective Mass formula is calculated badly somewhere, I don't know where. I got it right on paper, but on Excel I had trouble with it. So regarding that issue: Agreed. Effective Mass is wrong.[...]

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I often have a devil of a time translating known working formulae into functional Excel expressions, too. I usually wind up separating portions of a a long formula into small segments, each in its own cell, which allows me to see if any one portion is wildly out of range.

This is an ambitious project, so it's not surprising that it's giving you fits.

To explain, I 'derived' the formula from my copy of the Physics and Technology of Tennis, like most of my formulae. Originally, I had to make up a few 'control' variables, such as the location of impact on the racquet face, but then I noted that they had a more... direct way of doing it, so I instead used that as much as possible.

Before, I had kept my mouth shut because Ajm usually knows more than I do about this stuff, but that's how I got my results.

It is easy to adjust total weight, but it is not easy to change weight locations. Most people wrap it on the handle and on 9/3 locations. So can you make the weight locations as inputs and make swingweight and final weight outputs?